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%I #18 Jan 04 2021 18:49:16
%S 1,1,0,1,1,1,2,2,3,3,4,5,6,7,8,10,12,14,16,19,23,26,30,35,42,47,54,62,
%T 73,82,94,107,124,139,158,179,206,230,260,293,334,372,420,470,532,591,
%U 664,740,835,924,1034,1148,1288,1422,1588,1756,1962,2161,2404
%N Number of strict integer partitions of n in which the even parts appear as often at even positions as at odd positions.
%H Alois P. Heinz, <a href="/A300788/b300788.txt">Table of n, a(n) for n = 0..4000</a> (first 291 terms from Fausto A. C. Cariboni)
%e The a(9) = 3 strict partitions: (9), (621), (531). Missing are: (81), (72), (63), (54), (432).
%t cobal[y_]:=Sum[(-1)^x,{x,Join@@Position[y,_?EvenQ]}];
%t Table[Length[Select[IntegerPartitions[n],cobal[#]===0&&UnsameQ@@#&]],{n,0,40}]
%Y Cf. A000712, A000898, A001405, A026010, A045931, A063886, A097613, A130780, A171966, A239241, A300787, A300789.
%K nonn
%O 0,7
%A _Gus Wiseman_, Mar 12 2018
%E a(41)-a(58) from _Alois P. Heinz_, Mar 13 2018